In the given diagram, two circles pass through each other's center. If the radius of each circle is 2, then what is the perimeter of the region marked B?

Two circles with centres A and A' and having radius = 2 cm

$$\angle$$ BAC = $$120^\circ$$ [since ABA' forms a equilateral triangle] and length of an arc = $$\frac{\theta}{360^\circ}\times2\pi r$$

Perimeter of shaded portion = $$2\times($$ length of arc BC$$)$$

= $$2\times(\frac{120^\circ}{360^\circ}\times2\pi r)$$

= $$2\times(\frac{1}{3}\times2\pi\times2)$$

= $$2\times\frac{4\pi}{3}=\frac{8\pi}{3}$$

=> Ans - (A)